Mirror symmetry and an exact calculation of an (N - 2)-point correlation function on a Calabi-Yau manifold embedded in CPN-1

Masao Jinzenji, Masaru Nagura

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3 Citations (Scopus)

Abstract

We consider an (N - 2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of the Fermat type) in CPN-1 and its mirror manifold. We introduce an (N -2)-point correlation function (generalized Yukawa coupling) and evaluate it both by solving the Picard-Fuchs equation for period integrals in the mirror manifold and by explicitly calculating the contribution of holomorphic maps of degree 1 to the Yukawa coupling in the Calabi-Yau manifold using the method of algebraic geometry. In enumerating the holomorphic curves in the general-dimensional Calabi-Yau manifolds, we extend the method of counting rational curves on the Calabi-Yau three-fold using the Shubert calculus on Gr(2, N). The agreement of the two calculations for the (N - 2)-point function establishes "the mirror symmetry at the correlation function level" in the general-dimensional case.

Original languageEnglish
Pages (from-to)1217-1252
Number of pages36
JournalInternational Journal of Modern Physics A
Volume11
Issue number7
DOIs
Publication statusPublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics
  • Astronomy and Astrophysics

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